Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917159146356736 |
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| author | Salazar, Domingos S. P. |
| author_facet | Salazar, Domingos S. P. |
| contents | We show that any Petz $f$-divergence (where $f$ is operator convex) between quantum states admits a universal $χ^2$-mixture representation: the distinguishability of $ρ$ from $σ$ is obtained as a positive superposition of quadratic contrasts $χ^2_λ$, with nonnegative weights $w_f(λ)$ determined explicitly from the Stieltjes representation of the generator $f$. This identifies $χ^2_λ$ as atomic building blocks for quantum $f$-divergences and yields closed-form $w_f$ for canonical choices (relative entropy/KL, Hellinger/Bures, R'{e}nyi). By mapping $χ^2_λ$ into a classical Pearson $χ^2$, we leverage the Chapman-Robbins variational representation and obtain a tight and universal quantum thermodynamic uncertainty relation: any $f$-divergence is lower bounded by a function of the statistics of quantum observables (mean and variance), reproducing previous and novel results in quantum thermodynamics as applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences Salazar, Domingos S. P. Quantum Physics Statistical Mechanics We show that any Petz $f$-divergence (where $f$ is operator convex) between quantum states admits a universal $χ^2$-mixture representation: the distinguishability of $ρ$ from $σ$ is obtained as a positive superposition of quadratic contrasts $χ^2_λ$, with nonnegative weights $w_f(λ)$ determined explicitly from the Stieltjes representation of the generator $f$. This identifies $χ^2_λ$ as atomic building blocks for quantum $f$-divergences and yields closed-form $w_f$ for canonical choices (relative entropy/KL, Hellinger/Bures, R'{e}nyi). By mapping $χ^2_λ$ into a classical Pearson $χ^2$, we leverage the Chapman-Robbins variational representation and obtain a tight and universal quantum thermodynamic uncertainty relation: any $f$-divergence is lower bounded by a function of the statistics of quantum observables (mean and variance), reproducing previous and novel results in quantum thermodynamics as applications. |
| title | Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2511.10817 |